Question

A block of mass $2.0\,kg$ moving at $2.0\,m/s$ collides head on with another block of equal mass kept at rest. Find the maximum possible loss in kinetic energy(in joule) due to the collision.

Answer 1

Let us first get some idea about the law of conservation of momentum. One of the most well-known rules in physics is the conservation of momentum.The conservation of momentum principle states that a system's overall momentum is always conserved.

Complete step by step answer:
Unless an external force is applied, the overall momentum of two or more bodies in an isolated system operating on each other remains constant. As a result, neither the creation nor the destruction of momentum is possible.

Let see about Collision. A collision is defined in physics as any occurrence in which two or more bodies exert forces on each other in a brief period of time. Although the most common meaning of the word collision is an incident in which two or more objects clash violently, the scientific meaning of the phrase has nothing to do with the magnitude of the force.

In contrast to an elastic collision, an inelastic collision occurs when the kinetic energy is not conserved due to internal friction. When macroscopic bodies collide, some kinetic energy is converted into atomic vibrational energy, generating a heating effect and deformation of the bodies. Now let us come to problem:
Given: Mass of block$= 2\,kg$
The speed of the block is $= 2\,m/s$
Mass of $2nd$ block $= 2\,kg$
Let final velocity of $2nd$ block $= 2v$
By using the law of conservation of momentum.
${p_i} = {p_f}$
$2 \times 2 = (2 + 2)v$
$\Rightarrow {v^1} = 1\,m/s$
Loss in K.E. in inelastic collision
$\Delta KE = \dfrac{1}{2}m{v^2} - \dfrac{1}{2}(m + m){v^{'2}}$
$\Rightarrow \Delta KE= \dfrac{1}{2} \times 2 \times {(2)^2} - \dfrac{1}{2}(2 + 2) \times {(1)^2} \\\ \Rightarrow \Delta KE = 4 - 2 \\\ \therefore \Delta KE = 2\,J$

Hence, the maximum possible loss in kinetic energy(in joule) due to the collision is 2 J.

Note: Only along this line does the internal force of collision act during contact, therefore Newton's coefficient of restitution is determined. Collisions can be elastic, in which case they conserve both momentum and kinetic energy, or inelastic, in which case they conserve only momentum.